Cluster analysis - Levene's test fails


I am trying to segment people into clusters based on seven index variables (psycographic factors).

I formed five nice clusters (used K means clustering) but in ANOVA Levene's test is significant in almost all of the variables. I tried a bit different combinations of index variables, left some of them out, tried different amount of clusters, but the problem still exists.

Is there any way to fix it and be able to form clusters?